Cannot Delete Application Pool

If you open the Application Pool "tree" you should see which applications are associated to that pool. Of course, if all your application use the "Standard Application" name, this information has no value. So, when I create new applications, I always give them a meaningful name.

Second tip: you could give IIS Metabase Analyzer a try:

As the name implies, the application looks at IIS Metabase information to determine which IIS Web applications are running under which IIS Web sites. Additionally, it determines which Application Pools those websites and web applications are running under. When a version conflict is detected, IIS Metabase Analyzer alerts you to it and then it's up to you to fix the issue with the IIS Management tools.